Systematic Reviews:

1
Systematic Reviews Methods and Procedures
George A. Wells Editor, Cochrane Musculoskeletal
Review Group Department of Epidemiology and
Community Medicine University of Ottawa Ottawa,
Ontario, Canada
2
Meta-analysis

• Meta-analysis is a statistical analysis of a
  collection of studies
• Meta-analysis methods focus on contrasting and
  comparing results from different studies in
  anticipation of identifying consistent patterns
  and sources of disagreements among these results
• Primary objective
• Synthetic goal (estimation of summary effect)
  vs
• Analytic goal (estimation of differences)

3

• Systematic Review
• the application of scientific strategies that
  limit bias to the systematic assembly, critical
  appraisal and synthesis of all relevant studies
  on a specific topic
• Meta-Analysis
• a systematic review that employs statistical
  methods to combine and summarize the results of
  several studies

4
Features of narrative reviews and systematic
reviews
NARRATIVE SYSTEMATIC
QUESTION Broad Focused SOURCES/ Usually
unspecified Comprehensive SEARCH Possibly
biased explicit SELECTION Unspecified
biased?Criterion-based uniformly
applied APPRAISAL Variable Rigourous SYNTHESIS
Usually qualitative Quantitative INFERENCE
Sometimes Usually evidence-
evidence-based based
5
Steps of a Cochrane Systematic Review

• Clearly formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

6

• What is the study objective
• to validate results in a large population
• to guide new studies
• Pose question in both biologic and health care
  terms specifying with operational definitions
• population
• intervention
• outcomes (both beneficial and harmful)

7
Inclusion Criteria

• Study design
• Population
• Interventions
• Outcomes

8
Steps of a Cochrane Systematic Review

• Clearly formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

9

• Need a well formulated and co-ordinated effort
• Seek guidance from a librarian
• Specify language constraints
• Requirements for comprehensiveness of search
  depends on the field and question to be addressed
• Possible sources include
• computerized bibliographic database
• review articles
• abstracts
• conference proceedings
• dissertations
• books
• experts
• granting agencies
• trial registries
• industry
• journal handsearching

10

• Procedure
• usually begin with searches of biblographic
  reports (citation indexes, abstract databases)
• publications retrieved and references therein
  searched for more references
• as a step to elimination of publication bias need
  information from unpublished research
• databases of unpublished reports
• clinical research registries
• clinical trial registries
• unpublished theses
• conference indexes

Published Reports (publication bias ie.
tendency to publish statistically significant
results)
11
Steps of a Cochrane Systematic Review

• Clearly formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

12
Study Selection

• 2 independent reviewers select studies
• Selection of studies addressing the question
  posed based on a priori specification of the
  population, intervention, outcomes and study
  design
• Level of agreement kappa
• Differences resolved by consensus
• Specify reasons for rejecting studies

13
Data Extraction

• 2 independent reviewers extract data using
  predetermined forms
• Patient characteristics
• Study design and methods
• Study results
• Methodologic quality
• Level of agreement kappa
• Differences resolved by consensus

14
Data Extraction .

• Be explicit, unbiased and reproducible
• Include all relevant measures of benefit and harm
  of the intervention
• Contact investigators of the studies for
  clarification in published methods etc.
• Extract individual patient data when published
  data do not answer questions about intention to
  treat analyses, time-to-event analyses,
  subgroups, dose-response relationships

15
Steps of a Cochrane Systematic Review

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

16
Description of Studies

• Size of study
• Characteristics of study patients
• Details of specific interventions used
• Details of outcomes assessed

17
Methodologic Quality Assessment

• Can use as
• threshold for inclusion
• possible explanation form heterogeneity
• Base quality assessments on extent to which bias
  is minimized
• Make quality assessment scoring systems
  transparent and parsimonious
• Evaluate reproducibility of quality assessment
• Report quality scoring system used

18
Quality Assessment Example
indicates that randomization was appropriate (
eg
Random numbers were computer generated)
19
Steps of a Cochrane Systematic Review

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

20
Outcome
Discrete (event)
Continuous (measured)
Mean Standardized Difference Mean
Difference (MD) (SMD)
Odds Relative Risk Ratio Risk
Difference (OR) (RR) (RD)
(Basic Data)
(Basic Data)
Overall Estimate Fixed Effects Random Effects
Overall Estimate Fixed Effects Random Effects
21
Effect measures discrete data

• P1 event rate in experimental group
• P2 event rate in control group
• RD Risk difference P2 - P1
• RR Relative risk P1 / P2
• RRR Relative risk reduction (P2-P1)/P2
• OR Odds ratio P1/(1-P1)/P2/(1-P2)
• NNT No. needed to treat 1 / (P2-P1)

22
Example

• Experimental event rate 0.3
• Control event rate 0.4
• RD 0.4 - 0.3 0.1
• RR 0.3 / 0.4 0.75
• RRR (0.4 - 0.3) / 0.4 0.25
• OR (0.3/0.7)/(0.4/0.6) 0.64
• NNT 1 / (0.4 - 0.3) 10

23
Discrete - Odds Ratio (OR)
Event No event Experimental a b
ne Control c d nc
Odds number of patients experiencing
event number of patients not experiencing
event Odds ratio Odds in Experimental
group Odds in Control group
Basic Data a/ne c/nc
24
Discrete - Odds Ratio Example
Event No event Experimental 13 33
46 Control 7 31 38
Basic Data 13/46 7/38
25
Discrete - Relative Risk (RR)
Event No event Experimental a b
ne Control c d nc
Risk number of patients experiencing
event number of patients Risk Ratio Risk in
Experimental group Risk in Control group
Basic Data a/ne c/nc
26
Discrete - Relative Risk - Example
Event No event Experimental 13 33
46 Control 7 31 38
Basic Data 13/46 7/38
27
Discrete - Risk Difference (RD)
Event No event Experimental a b
ne Control c d nc
Risk number of patients experiencing
event number of patients Risk
Difference (Risk in Experimental group) - (Risk
in Control group)
RD Pe- Pc
Basic Data a/ne c/nc
28
Discrete - Risk Difference - Example
Event No event Experimental 13 33
46 Control 7 31 38
RD Pe- Pc 13/46 - 7/38 0.098
Basic Data 13/46 7/38
29
Discrete - Odds Ratio
(O)
Event No event Experimental a b
ne Control c d nc
Estimator
Standard Error
100(1- ) CI
30
Discrete - Relative Risk
(R)
Event No event Experimental a b
ne Control c d nc
Estimator
Standard Error
100(1- ) CI
31
Discrete - Risk Difference
(D)
Event No event Experimental a b
ne Control c d nc
Estimator
Standard Error
100(1- ) CI
32
When to use OR / RR / RD
OR vs RR Odds Ratio ? Relative Risk if event
occurs infrequently (i.e. a and c small
relative to b and d) RR a(cd) ? ad
OR (ab)c bc Odds Ratio gt Relative Risk if
event occurs frequently RD vs RR When
interpretation in terms of absolute difference is
better than in relative terms (eg. Interest in
absolute reduction in adverse events)
33
(No Transcript)
34
Continuous Data - Mean Difference (MD)
number mean standard deviation Experimental ne
se Control nc sc
35
Continuous Data - Standardized Mean Difference
(SMD)
number mean standard deviation Experimental ne
se Control nc sc
36
When to use MD / SMD

• Mean Difference
• When studies have comparable outcome measures
  (ie. Same scale, probably same length of
  follow-up)
• A meta-analysis using MDs is known as a weighted
  mean difference (WMD)
• Standardized Mean Difference
• When studies use different outcome measurements
  which address the same clinical outcome (eg
  different scales)
• Converts scale to a common scale number of
  standard deviations

37
Example Combining different scales for Swollen
Joint Count
38
Sources of Variation over Studies

• True inter-study variation may exist
  (fixed/random-effects model)
• Sampling error may vary among studies (sample
  size)
• Characteristics may differ among studies
  (population, intervention)

39
Modelling Variation

• Parameter of interest (quantifies average
  treatment effect)
• Number of independent studies k
• Summary Statistic Yi (i1,2,,k)
• Large sample size asymptotic normal distribution

Fixed-effects model vs Random-effects model
40
Fixed-Effects Model

• Outcome Yi from study i is a sample from a
  distribution with mean
• (ie. common mean across studies)
• Yi are independently distributed as N ( ,
  ) (i1,2,,k) where Var(Yi ) and
  assume E(Yi)

41
Fixed-Effects Model
x
42
Random-Effects Model

• Outcome Yi from study i is a sample from a
  distribution with mean
• (ie. study-specific means)
• Yi are independently distributed as N ( ,
  ) (i1,2,,k) where Var(Yi ) and
  assume E(Yi)
• is a realization from a distribution of
  effects with mean
• are independently distributed as N ( ,
  ) (i1,2,,k) where
• Var ( ) is the inter-study variation
• is the average treatment effect

43
Random-Effects Model
x
44
Random-Effects Model ..
Estimating Average Study Effect

• after averaging study-specific effects,
  distribution of Yi is N ( , )
• although is parameter of interest, must
  be considered and estimated

Estimating Study-Specific Effects

• distribution of conditional on observed
  data, and is N (
  )
• where Fi is the shrinkage factor for the ith
  study

45
Modelling Variation

• Studies are stratified and then combined to
  account for differences in sample size and study
  characteristics
• A weighted average of estimates from each study
  is calculated
• Question of whether a common or study-specific
  parameter is to be estimated remains .
  Procedure
• perform test of homogeneity
• if no significant difference use fixed-effects
  model
• otherwise identify study characteristics that
  stratifies studies into subsets with homogeneous
  effects or use random effects model

46
Fixed Effects Model

• Require from each study
• effect estimate and
• standard error of effect estimate
• Combine these using a weighted average
• pooled estimate sum of (estimate ? weight)
  
• sum of weights
• where weight 1 / variance of estimate
• Assumes a common underlying effect behind every
  trial

47
Fixed-Effects Model General Scheme
Study Measure Std Error Weight 1 Y1 s1 W1 2 Y
2 s2 W2 . . . . . . . . . . . . k Yk sk
Wk (no association Yi0)
Overall Measure
48
Chi-Square Tests
1
2
1
If large association
2
If large heterogeneity
49
Features in Graphic Display

• For each trial
• estimate (square)
• 95 confidence interval (CI) (line)
• size (square) indicates weight allocated
• Solid vertical line of no effect
• if CI crosses line then effect not significant
  (pgt0.05)
• Horizontal axis
• arithmetic RD, MD, SMD
• logarithmic OR, RR
• Diamond represents combined estimate and 95 CI
• Dashed line plotted vertically through combined
  estimate

50
Odds Ratio
Three methods for combining (1)
Mantel-Haenszel method (2) Petos method (3)
Maximum likelihood method Relative Risk Risk
Difference
51
Peto Odds Ratio
Mantel-Haenszel Odds Ratio
52
Relative Risk
53
Risk Difference
54
Weighted Mean Difference

• Standardized Mean Difference

55
Weighted Mean Difference
Standardized Mean Difference
56
Heterogeneity

• Define meaning of heterogeneity for each review
• Define a priori the important degree of
  heterogeneity (in large data sets trivial
  heterogeneity may be statistically significant)
• If heterogeneity exists examine potential sources
  (differences in study quality, participants,
  intervention specifics or outcome
  measurement/definition)
• If heterogeneity exists across studies, consider
  using random effects model
• If heterogeneity can be explained using a priori
  hypotheses, consider presenting results by these
  subgroups
• If heterogeneity cannot be explained, proceed
  with caution with further statistical aggregation
  and subgroup analysis

57
Heterogeneity How to Identify it

• Common sense
• are the patients, interventions and outcomes in
  each of the included studies sufficiently similar
• Exploratory analysis of study-specific estimates
• Statistical tests

58
Heterogeneity How to deal with it
Lau et al. 1997
59
Heterogeneity Exploring it

• Subgroup analyses
• subsets of trials
• subsets of patients
• SUBGROUPS SHOULD BE PRE-SPECIFIED TO AVOID BIAS
• Meta-regression
• relate size of effect to characteristics of the
  trials

60
Exploring Heterogeneity subgroup analysis
61
Exploring Heterogeneity subgroup analysis
62
Random Effects Model

• Assume true effect estimates really vary across
  studies
• Two sources of variation
• within studies (between patients)
• between studies (heterogeneity)
• What the software does
• Revise weights to take into account both
  components of variation
• weight 1
• varianceheterogeneity
• When heterogeneity exists we get
• a different pooled estimate (but not necessarily)
  with a different interpretation
• a wider confidence interval
• a larger p-value

63
Random Effects Model
If is known then MLE of is
If is unknown three common methods of
inference can be used Restricted Maximum
Likelihood (REML) Bayesian Method of
Moments (MOM)
64
Method of Moments (Random effects model)
Study Measure Weight (FE) Weight (RE) 1 Y1
W1 w1(w1-1 )-1 2 Y2 W2 w2(w2-1
)-1 . . . . . . . . . . . . k Yk Wk
wk(wk-1 )-1
Overall Measure
65
Effect of model choice on study weights
Larger studies receive proportionally less
weight in RE model than in FE model
66
Fixed vs Random Effects Discrete Data

Fixed Effects
Random Effects
67
Fixed vs Random Effects Continuous Data

Fixed Effects
Random Effects
68
Omission of Outlier - Chestnut Study
69
Analysis

• Include all relevant and clinically useful
  measures of treatment effect
• Perform a narrative, qualitative summary when
  data are too sparse, of too low quality or too
  heterogeneous to proceed with a meta-analysis
• Specify if fixed or random effects model is used
• Describe proportion of patients used in final
  analysis
• Use confidence intervals
• Include a power analysis
• Consider cumulative meta-analysis (by order of
  publication date, baseline risk, study quality)
  to assess the contribution of successive studies

70
Steps of a Cochrane Systematic Review

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

71
Subgroup Analyses

• Pre-specify hypothesis-testing subgroup analyses
  and keep few in number
• Label all a posteriori subgroup analyses
• When subgroup differences are detected, interpret
  in light of whether they are
• established a priori
• few in number
• supported by plausible causal mechanisms
• important (qualitative vs quantitative)
• consistent across studies
• statistically significant (adjusted for multiple
  testing)

72
Sensitivity Analyses

• Test robustness of results relative to key
  features of the studies and key assumptions and
  decisions
• Include tests of bias due to retrospective nature
  of systematic reviews (eg.with/without studies of
  lower methodologic quality)
• Consider fragility of results by determining
  effect of small shifts in number of events
  between groups
• Consider cumulative meta-analysis to explore
  relationship between effect size and study
  quality, control event rates and other relevent
  features
• Test a reasonable range of values for missing
  data from studies with uncertain results

73
Funnel Plot

• Scatterplot of effect estimates against sample
  size
• Used to detect publication bias
• If no bias, expect symmetric, inverted funnel
• If bias, expect asymmetric or skewed shape

x x x x
x x x x x x x x
x x x
x x x x x x x
Suggestion of missing small studies
74
Funnel Plot Example 1 Prophylaxis of NSAID
induced Gastric Ulcers
700
600
500
400
Sample Size
300
Intervention
200
100
H2-Blockers
0
1.2
1.0
.8
.6
.4
.2
0.0
Effect Size (RR)
75
Funnel Plot Example 2 Alendronate for
Postmenopausal Osteoporosis
2500
2000
WMD of change in lumbar bone mineral density
1500
Sample Size
1000
500
0
0
5
10
Weighted Mean Difference
76
Steps of a Cochrane Systematic Review

• Well formulated question
• Comprehensive data search
• Unbiased selection and extraction process
• Critical appraisal of data
• Synthesis of data
• Perform sensitivity and subgroup analyses if
  appropriate and possible
• Prepare a structured report

77
Presentation of Results

• Include a structured abstract
• Include a table of the key elements of each study
• Include summary data from which the measures are
  computed
• Employ informative graphic displays representing
  confidence intervals, group event rates, sample
  sizes etc.

78
Interpretation of Results

• Interpret results in context of current health
  care
• State methodologic limitations of studies and
  review
• Consider size of effect in studies and review,
  their consistency and presence of dose-response
  relationship
• Consider interpreting results in context of
  temporal cumulative meta-analysis
• Interpret results in light of other available
  evidence
• Make recommendations clear and practical
• Propose future research agenda (clinical and
  methodological requirements)

79
Generic Inferential Framework
80
Generic inferential framework

• (1) Conceptually, think of a generic effect
  size statistic T
• (2) corresponding effect size parameter ?
• (3) associated standard error SE(T), square root
  of variance
• (4) for some effect sizes, some suitable
  transformation may be needed to make inference
  based on normal distribution theory

81
Generic inferential framework ...

• (A) Fixed-Effects Model (FEM)
• Assume a common effect size
• Obtain average effect size as a weighted mean
  (unbiased)
• Optimal weight is reciprocal of variance
  (inverse variance weighted method)

82
Generic inferential framework ...

• Variances inversely proportional to within-study
  sample sizes
• what is the effect of larger studies in
  calculating weights?
• may also weigh by quality index, q, scaled from
  0 to 1

83
Generic inferential framework ...

• Average effect size has conditional variance (a
  function of conditional variances of each effect
  size, quality index, )
• e.g.. V 1/total weight
• Multiply the resulting standard error by
  appropriate critical value (1.96, 2.58, 1.645)
• Construct confidence interval and/or test
  statistic

84
Generic inferential framework ...

• Test the homogeneity assumption using a weighted
  effect size sums of squares of deviations, Q
• If Q exceeds the critical value of chi-square at
  k-1 d.f. (k number of studies), then observed
  between-study variance significantly greater than
  what would be expected under the null hypothesis

85
Generic inferential framework ...

• When within-study sample sizes are very large, Q
  may be rejected even when individual effect size
  estimates do not differ much
• One can take different courses of action when Q
  is rejected (see next page)

86
Generic inferential framework ...

• Methodologic choices in dealing with
  heterogeneous data

87
Generic inferential framework ...

• (B) Random-Effects Model (REM)
• Total variability of an observed study effect
  size reflects within and between variance (extra
  variance component)
• If between-studies variance is zero, equations of
  REM reduce to those of FEM
• Presence of a variance component which is
  significantly different from zero may be
  indicative of REM

88
Generic inferential framework ...

• Once significance of variance component is
  established (e.g.. Q test for homogeneity of
  effect size),
• its magnitude should be estimated
• variance components can be estimated in many
  ways!
• the most commonly used method is the so-called
  the DerSimonian-Laird method which is based on
  method-of-moments approach
• Compute random effects weighted mean as an
  estimate of the average of the random effects in
  the population
• construct confidence interval and conduct
  hypothesis tests as before (new variance and thus
  new weights!!!)

89
Correlation Coefficient
90
Example Correlation coefficient

• A measure of association more popular in
  cross-sectional observational studies than in
  RCTs is Pearsons correlation coefficient, r
  given by
• X and Y must be continuous (e.g. blood pressure
  and weight)
• r lies between -1 to 1
• not available in RevMan / MetaView at this time

91
Correlation coefficient (contd)

• Following the generic framework discussed
  earlier
• the effect size statistic is r
• the corresponding effect size parameter is the
  underlying population correlation coefficient, ?
• in this case, a suitable transformation is needed
  to achieve approximate normality of effect size
• inference is conducted on the scale of the
  transformed variable and final results are
  back-transformed to the original scale

92
Correlation coefficient (contd)

• Assuming X and Y have a bivariate normal
  distribution, the Fishers Z transformed variable
• has, for large sample, an approximate normal
  distribution with mean of
• and a variance of
• Hence, weighting factor associated with Z is W
  1/Var n-3.

93
Correlation coefficient (contd)

• meta-analysis is carried out on Z-transformed
  measures and final results are transformed back
  to the scale of correlation using

94
Numerical Example

• Source Fleiss J., Statistical Methods in Medical
  Research 1993 2 121 -- 145.
• correlation coefficients reported by 7
  independent studies in education are included in
  the meta-analysis
• Comparison association between a characteristic
  of the teacher and the mean measure of his or her
  students achievement

95
Example Fleiss (1993)
__________________________________________ Study
n r Z W WZ
WZ2
1 15 -0.073 -0.073 12
-0.876 0.064 2 16 0.308 0.318 13
4.134 1.315 3 15 0.481 0.524 12
6.288 3.295 4 16 0.428 0.457 13
5.941 2.715 5 15 0.180 0.182 12
2.184 0.397 6 17 0.290 0.299 14
4.186 1.252 7 __ 15 0.400 0.424 _ 12
___5.088 2.157__ Sum 88 26.945
11.195
Z Fishers Z-transformation of r W
n-3
Q 2.94 on 6 df is not statistically significant.
96
Results and discussions

• No evidence for heterogeneous association across
  studies
• Fixed effect analysis may be undertaken
• Questions
• Would a random effect analysis as shown earlier
  produce a different numerical value for the
  combined correlation coefficient?
• How would the weights be modified to carry out a
  REM?

97
Results and discussions (contd)

• the weighted mean of Z is
• the approximate standard error of the combined
  mean is

98
Results and discussions (contd)

• Test of significance is carried out using
• this value exceeds the critical value 1.96
  (corresponding to 5 level of significance), so
  we conclude that average value of Z (hence the
  average correlation) is statistically significant

99
Results and discussions (contd)

• 95 confidence interval for ? is
• Transforming back to the original scale, a 95 CI
  for the parameter of interest, ?, is
• again confirming a significant association

100
Critical Appraisal of a Systematic Review
101
(A) The Message

• Does the review set out to answer a precise
  question about patient care?
• Should be different from an uncritical
  encyclopedic presentation

102
(B) The Validity

• Have studies been sought thoroughly
• Medline and other relevant bibliographic database
  
• Cochrane controlled clinical trials register
• Foreign language literature
• "Grey literature" (unpublished or un-indexed
  reports theses, conference proceedings, internal
  reports, non-indexed journals, pharmaceutical
  industry files)
• Reference chaining from any articles found
• Personal approaches to experts in the field to
  find unpublished reports
• Hand searches of the relevant specialized
  journals.

103
Validity (contd)

• Have inclusion and exclusion criteria for studies
  been stated explicitly, taking account of the
  patients in the studies, the interventions used,
  the outcomes recorded and the methodology?

104
Validity (contd)

• Have the authors considered the homogeneity of
  the studies the idea that the studies are
  sufficiently similar in their design,
  interventions and subjects to merit combination.
• this is done either by eyeballing graphs like the
  forest plot or by applications of chi-square
  tests (Q test)

105
(C) The Utility

• The various studies may have used patients of
  different ages or social classes, but if the
  treatment effects are consistent across the
  studies, then generalisation to other groups or
  populations is more justified.

106
Utility (contd)

• Be wary of sub-group analyses where the authors
  attempt to draw new conclusions by comparing the
  outcomes for patients in one study with the
  patients in another study
• Be wary of "data-dredging" exercises, testing
  multiple hypotheses against the data, especially
  if the hypotheses were constructed after the
  study had begun data collection.

107
Utility (contd)

• One may also want to ask
• Were all clinically important outcomes
  considered?
• Are the benefits worth the harms and costs?